TSTP Solution File: LCL499+1 by Duper---1.0
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% File : Duper---1.0
% Problem : LCL499+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:09:58 EDT 2023
% Result : Theorem 4.36s 4.55s
% Output : Proof 4.36s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL499+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 18:51:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.36/4.55 SZS status Theorem for theBenchmark.p
% 4.36/4.55 SZS output start Proof for theBenchmark.p
% 4.36/4.55 Clause #0 (by assumption #[]): Eq (Iff modus_ponens (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y)) True
% 4.36/4.55 Clause #15 (by assumption #[]): Eq (Iff kn1 (∀ (P : Iota), is_a_theorem (implies P (and P P)))) True
% 4.36/4.55 Clause #21 (by assumption #[]): Eq (Iff r1 (∀ (P : Iota), is_a_theorem (implies (or P P) P))) True
% 4.36/4.55 Clause #23 (by assumption #[]): Eq (Iff r3 (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P)))) True
% 4.36/4.55 Clause #27 (by assumption #[]): Eq (op_and → ∀ (X Y : Iota), Eq (and X Y) (not (or (not X) (not Y)))) True
% 4.36/4.55 Clause #29 (by assumption #[]): Eq (op_implies_or → ∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True
% 4.36/4.55 Clause #31 (by assumption #[]): Eq op_implies_or True
% 4.36/4.55 Clause #32 (by assumption #[]): Eq op_and True
% 4.36/4.55 Clause #34 (by assumption #[]): Eq modus_ponens True
% 4.36/4.55 Clause #35 (by assumption #[]): Eq r1 True
% 4.36/4.55 Clause #37 (by assumption #[]): Eq r3 True
% 4.36/4.55 Clause #43 (by assumption #[]): Eq (Not kn1) True
% 4.36/4.55 Clause #45 (by clausification #[0]): Or (Eq modus_ponens False)
% 4.36/4.55 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 4.36/4.55 Clause #64 (by clausification #[43]): Eq kn1 False
% 4.36/4.55 Clause #65 (by clausification #[45]): ∀ (a : Iota),
% 4.36/4.55 Or (Eq modus_ponens False)
% 4.36/4.55 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 4.36/4.55 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota),
% 4.36/4.55 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 4.36/4.55 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota),
% 4.36/4.55 Or (Eq modus_ponens False)
% 4.36/4.55 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 4.36/4.55 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota),
% 4.36/4.55 Or (Eq modus_ponens False)
% 4.36/4.55 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 4.36/4.55 Clause #69 (by forward demodulation #[68, 34]): ∀ (a a_1 : Iota),
% 4.36/4.55 Or (Eq True False)
% 4.36/4.55 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 4.36/4.55 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 4.36/4.55 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 4.36/4.55 Clause #83 (by clausification #[15]): Or (Eq kn1 True) (Eq (∀ (P : Iota), is_a_theorem (implies P (and P P))) False)
% 4.36/4.55 Clause #85 (by clausification #[83]): ∀ (a : Iota), Or (Eq kn1 True) (Eq (Not (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a))))) True)
% 4.36/4.55 Clause #86 (by clausification #[85]): ∀ (a : Iota), Or (Eq kn1 True) (Eq (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a)))) False)
% 4.36/4.55 Clause #87 (by forward demodulation #[86, 64]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a)))) False)
% 4.36/4.55 Clause #88 (by clausification #[87]): ∀ (a : Iota), Eq (is_a_theorem (implies (skS.0 6 a) (and (skS.0 6 a) (skS.0 6 a)))) False
% 4.36/4.55 Clause #92 (by clausification #[21]): Or (Eq r1 False) (Eq (∀ (P : Iota), is_a_theorem (implies (or P P) P)) True)
% 4.36/4.55 Clause #96 (by clausification #[92]): ∀ (a : Iota), Or (Eq r1 False) (Eq (is_a_theorem (implies (or a a) a)) True)
% 4.36/4.55 Clause #97 (by forward demodulation #[96, 35]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (or a a) a)) True)
% 4.36/4.55 Clause #98 (by clausification #[97]): ∀ (a : Iota), Eq (is_a_theorem (implies (or a a) a)) True
% 4.36/4.55 Clause #99 (by superposition #[98, 70]): ∀ (a a_1 : Iota),
% 4.36/4.55 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (implies (or a_1 a_1) a_1) a)) False))
% 4.36/4.55 Clause #224 (by clausification #[29]): Or (Eq op_implies_or False) (Eq (∀ (X Y : Iota), Eq (implies X Y) (or (not X) Y)) True)
% 4.36/4.55 Clause #225 (by clausification #[224]): ∀ (a : Iota), Or (Eq op_implies_or False) (Eq (∀ (Y : Iota), Eq (implies a Y) (or (not a) Y)) True)
% 4.36/4.55 Clause #226 (by clausification #[225]): ∀ (a a_1 : Iota), Or (Eq op_implies_or False) (Eq (Eq (implies a a_1) (or (not a) a_1)) True)
% 4.36/4.57 Clause #227 (by clausification #[226]): ∀ (a a_1 : Iota), Or (Eq op_implies_or False) (Eq (implies a a_1) (or (not a) a_1))
% 4.36/4.57 Clause #228 (by forward demodulation #[227, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (implies a a_1) (or (not a) a_1))
% 4.36/4.57 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), Eq (implies a a_1) (or (not a) a_1)
% 4.36/4.57 Clause #244 (by clausification #[23]): Or (Eq r3 False) (Eq (∀ (P Q : Iota), is_a_theorem (implies (or P Q) (or Q P))) True)
% 4.36/4.57 Clause #250 (by clausification #[244]): ∀ (a : Iota), Or (Eq r3 False) (Eq (∀ (Q : Iota), is_a_theorem (implies (or a Q) (or Q a))) True)
% 4.36/4.57 Clause #251 (by clausification #[250]): ∀ (a a_1 : Iota), Or (Eq r3 False) (Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True)
% 4.36/4.57 Clause #252 (by forward demodulation #[251, 37]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True)
% 4.36/4.57 Clause #253 (by clausification #[252]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (or a a_1) (or a_1 a))) True
% 4.36/4.57 Clause #256 (by superposition #[253, 229]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (implies a a_1) (or a_1 (not a)))) True
% 4.36/4.57 Clause #328 (by clausification #[99]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies (or a_1 a_1) a_1) a)) False)
% 4.36/4.57 Clause #331 (by superposition #[328, 256]): ∀ (a : Iota), Or (Eq (is_a_theorem (or a (not (or a a)))) True) (Eq False True)
% 4.36/4.57 Clause #334 (by clausification #[331]): ∀ (a : Iota), Eq (is_a_theorem (or a (not (or a a)))) True
% 4.36/4.57 Clause #337 (by superposition #[334, 229]): ∀ (a : Iota), Eq (is_a_theorem (or (not a) (not (implies a (not a))))) True
% 4.36/4.57 Clause #338 (by forward demodulation #[337, 229]): ∀ (a : Iota), Eq (is_a_theorem (implies a (not (implies a (not a))))) True
% 4.36/4.57 Clause #425 (by clausification #[27]): Or (Eq op_and False) (Eq (∀ (X Y : Iota), Eq (and X Y) (not (or (not X) (not Y)))) True)
% 4.36/4.57 Clause #426 (by clausification #[425]): ∀ (a : Iota), Or (Eq op_and False) (Eq (∀ (Y : Iota), Eq (and a Y) (not (or (not a) (not Y)))) True)
% 4.36/4.57 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Or (Eq op_and False) (Eq (Eq (and a a_1) (not (or (not a) (not a_1)))) True)
% 4.36/4.57 Clause #428 (by clausification #[427]): ∀ (a a_1 : Iota), Or (Eq op_and False) (Eq (and a a_1) (not (or (not a) (not a_1))))
% 4.36/4.57 Clause #429 (by forward demodulation #[428, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (and a a_1) (not (or (not a) (not a_1))))
% 4.36/4.57 Clause #430 (by clausification #[429]): ∀ (a a_1 : Iota), Eq (and a a_1) (not (or (not a) (not a_1)))
% 4.36/4.57 Clause #431 (by forward demodulation #[430, 229]): ∀ (a a_1 : Iota), Eq (and a a_1) (not (implies a (not a_1)))
% 4.36/4.57 Clause #432 (by backward demodulation #[431, 338]): ∀ (a : Iota), Eq (is_a_theorem (implies a (and a a))) True
% 4.36/4.57 Clause #455 (by superposition #[432, 88]): Eq True False
% 4.36/4.57 Clause #460 (by clausification #[455]): False
% 4.36/4.57 SZS output end Proof for theBenchmark.p
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